Did you start with File > New > Labels? If so, there is an option to allow "syncronizing" the label content. You have to set the option when the label sheet is constructed. If the option is ON, there will be a small, floating button that will synchronize the content.

If you made your own labels, or started with a template sheet, then you probably have to copy them manually. That's not a big problem: copy one, select all, and paste. Or, paste to fill one row, then copy that into all the other rows.